\fdO'^ - Old Forge Coal Mines

140 GEOMETRY AND TRIGONOMETRY.
in the polygon, less two. As a regular dodecagon has 12
equal sides, the sum of the interior angles equals two right
angles X 10 ( = 12 — 2), or 20 right angles. Since there are
12 equal angles, the size of any one of them equals 20 ~- 12,
2
or 1— right angles,
o
(280) Equilateral triangle.
(281) No,
greater than the third side.
since the sum of the two smaller sides is not
(282) No, since the sum of the three smaller sides is not
greater than the fourth side.
j^ (283) Since the two angles A and C,
Fig. 1, are equal, the triangle is isosceles, and a
line drawn from the vertex B will bisect the line
A C, the length of which is 7 inches ; therefore,
AD=DC=1 = dl-in.
Ans.
(284) The length of the line = 4/12' - 9' + |/15*- 9»,
or 19.94 inches.
g
(285) The sum of the three angles is equal to — , or 2
right angles ; therefore, since the sum of two of them equals
K ^ K 'X
J of a right angle, the third angle must equal — — —, or — of
a right angle.
(286) One of the angles of an equiangular octagon is
equal to — of 12 right angles, or 1 — right angles, since the
sum of the interior angles of the equiangular octagon equals
12 right angles.
(287) The sum of the acute angles of a right-angled
triangle equals one right angle; therefore, if one of them
5 8 5 3
equals 5- of a right angle, the other equals — — -, or — of a
o 000
right angle.